G100 Upper Tail Probability of Chi-Squared Distribution

Function subprogram PROB computes the probability that a random variable having a $\chi 2$ -distribution with $N\; \ge 1$

degrees of freedom assumes a value which is larger than a given value $X\; \ge 0$ , i.e.

$Q(X|N)\; =\; \{12N\hspace{0.17em}\Gamma (\{12\}N)\}\hspace{0.17em}\int$_X^&inf;e^-{12}t t^{12}N-1 dt.

Structure:

FUNCTION subprogram
User Entry Names: PROB
External References: ERFC, DERFC (C300), MTLMTR (N002), ABEND (Z035)

Usage:

In any arithmetic expression, PROB(X,N) has the value $Q(X,N)$ .

PROB and X are of type REAL and N is of type INTEGER.

Method:

See Ref. 1, formulae Nr. 26.4.4, 26.4.5 and, for N>300, No. 26.4.14.

Accuracy:

For $N\; \le 300$ , PROB has an accuracy of about six digits. For $N>300$ , the accuracy decreases for $X>N$ with increasing X.

Error handling:

Error G100.1: .
Error G100.2: .
In both cases, the function value is set equal to zero, and a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

References:

1. M. Abramowitz and I.A. Stegun (eds.), Handbook of mathematical functions with formulas, graphs, and mathematcal tables, 9th printing with corrections, (Dover, New York 1972).

G101